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3170 IEEE TRANSACTIONS ON ELECTRON DEVICES, VOL. 58, NO. 9, SEPTEMBER 2011

Influence of Metal–Graphene Contact on theOperation and Scalability of Graphene

Field-Effect TransistorsPei Zhao, Student Member, IEEE, Qin Zhang, Member, IEEE, Debdeep Jena, and Siyuranga O. Koswatta

Abstract—We explore the effects of metal contacts on the op-eration and scalability of 2-D graphene field-effect transistors(GFETs) using detailed numerical device simulations based onthe nonequilibrium Green’s function formalism self-consistentlysolved with the Poisson equation at the ballistic limit. Our treat-ment of metal–graphene (M–G) contacts captures the follow-ing: 1) the doping effect due to the shift of the Fermi level ingraphene contacts and 2) the density-of-states (DOS) broadeningeffect inside graphene contacts due to metal-induced states (MIS).Our results confirm the asymmetric transfer characteristics inGFETs due to the doping effect by metal contacts. Furthermore,at higher M–G coupling strengths, the contact DOS broadeningeffect increases the on-current, while the impact on the minimumcurrent (Imin) in the OFF-state depends on the source-to-drainbias voltage and the work-function difference between grapheneand the contact metal. Interestingly, with scaling of the channellength, the MIS inside the channel has a weak influence on Imin

even at large M–G coupling strengths, while direct source-to-drain(S → D) tunneling has a stronger influence. Therefore, channellength scalability of GFETs with sufficient gate control will bemainly limited by direct S → D tunneling, and not by the MIS.

Index Terms—Density-of-states (DOS) broadening, graphenefield-effect transistors (GFETs), metal-induced states (MIS),source-to-drain (S → D) tunneling.

I. INTRODUCTION

G RAPHENE is a 2-D zero-bandgap material with carbonatoms arranged in a honeycomb lattice [1], [2]. A fi-

nite bandgap can be obtained through quantum confinementby cutting 2-D graphene into strips as graphene nanoribbons(GNRs). High-quality GNRs with acceptable edge uniformity,however, pose a technological challenge. However, monolayer2-D graphene can be achieved by means of mechanical ex-foliation of graphite, high-temperature sublimation of siliconfrom SiC substrates [3], or CVD growth on metal substrates

Manuscript received February 3, 2011; revised April 19, 2011; acceptedJune 1, 2011. Date of publication July 22, 2011; date of current versionAugust 24, 2011. The review of this paper was arranged by Editor M. A. Reed.

P. Zhao and D. Jena are with the Department of Electrical Engineering, Uni-versity of Notre Dame, Notre Dame, IN 46556 USA (e-mail: [email protected]).

Q. Zhang was with the Department of Electrical Engineering, University ofNotre Dame, Notre Dame, IN 46556 USA. She is now with the CMOS andNovel Devices Group, Semiconductor Electronics Division, National Instituteof Standards and Technology, Gaithersburg, MD 20899 USA.

S. O. Koswatta is with the IBM Research Division, T. J. Watson ResearchCenter, Yorktown Heights, NY 10598 USA.

Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TED.2011.2159507

[4], [5]. Although 2-D monolayer graphene lacks a bandgap,it still shows promising potential for applications in high-frequency devices that do not require a high on/off ratio asdemanded by digital logic [6]–[10]. Recently, many theoreticaland experimental works have studied the microscopic physicsof metal–graphene (M–G) contacts, which show that metal con-tacts could play a critical role on the device performance [11]–[22]. In this regard, theoretical studies based on the densityfunctional theory show that, when graphene is covered by ametal electrode, the Fermi level of graphene underneath willbe shifted [11], [12]. This behavior has also been observed inexperiments [13], [14]. However, the detailed influence of M–Gcontacts on the transport properties and, more importantly, onthe scalability of graphene field-effect transistors (GFETs) hasnot been addressed yet.

In this paper, we study the effect of M–G coupling on theoperation and the scalability of 2-D GFETs. Even though previ-ous simulation studies have explained the asymmetric transportcharacteristics in electrostatically doped graphene p-n junctions[23], experiments have indicated that M–G contacts themselvesmay also lead to asymmetric conduction in 2-D GFETs [13],[14]. In this paper, we confirm the latter observation by us-ing a self-consistent 2-D electrostatic solution of the GFETgeometry [24] which captures the metal-induced doping effect.M–G coupling could also lead to metal-induced states (MIS)inside the graphene channel, which is similar in origin to themetal-induced gap states in conventional metal–semiconductorcontacts [25]. Experiments have also confirmed that the impactof metal contacts on the channel potential extends into thechannel for several hundred nanometers [20]–[22]. Here, weconsider the influence of MIS on the scalability of GFETs andprovide detailed insights into the impact of metal contacts onGFET characteristics.

II. DEVICE MODEL AND THE SIMULATION APPROACH

The modeled device is shown in Fig. 1. The channel isassumed to be uniform graphene with a width W of 150 nm.At W = 150 nm, the current density (in milliamperes per mi-crometer) is similar to the 2-D analytical result, which justifiesthe effective 2-D limit of the modeled GFET. The top gateinsulator is tox = 1.5 nm thick and has a dielectric constantεox = 20. With such excellent dielectric assumptions, short-channel effects can be avoided in our model, and we can focus

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ZHAO et al.: INFLUENCE OF METAL–GRAPHENE CONTACT ON THE OPERATION AND SCALABILITY OF GFETs 3171

Fig. 1. Structure of modeled device. The graphene channel is fully covered bythe top gate. tox = 1.5 nm and εox = 20. The SiO2 substrate is 50 nm thickand is connected to ground. This dielectric assumption can avoid short-channeleffects, and it is used as the nominal condition.

on the effects from the M–G contacts (the impact of the oxidethickness will be discussed hereinafter). The SiO2 substrate is50 nm in thickness and connected to the ground. The simulatedarea is only the channel region (dashed rectangle in Fig. 1)with fixed boundary conditions at the source and the drain.The electrostatic solution procedure is described in [24]. Theeffective oxide thickness (EOT) of our modeled device is only0.3 nm; thus, the quantum capacitance (CQ) correspondingto the graphene density of states (DOS) cannot be ignored.Our simulations self-constantly solve both the transport and theelectrostatic parts; thus, the effect of quantum capacitance isnaturally captured. In other words, the total gate capacitanceCG is not simply equal to Cox but more generally to CG =(CoxCQ)/(Cox + CQ).

Here, the tight-binding model for ballistic transport in thechannel is assumed, and it is solved using a mode-space-based nonequilibrium Green’s function formalism [26]. Themode-space approach significantly reduces the computationalcost while still maintaining the accuracy, as has already beendemonstrated in simulations of MOSFET [27], carbon nanotubeFET [28], and GNR FET [29]. In our calculations, we assumethat the potential variation along the channel width directionis negligible. Based on this approximation, the electrostaticsis solved in 2-D, and the mode-space method yields accurateresults.

In this paper, the contact regions are assumed to be semi-infinitely long and comprised of a metal layer deposited on topof the graphene layer [11], [16]. In this M–G hybrid system(dotted rectangle in Fig. 1), the Fermi level of the grapheneunderneath is shifted, and the DOS is broadened due to theM–G coupling [11], [12]. The Fermi level shift in the con-tact regions is modeled by ΔEcontact = EF − EDirac, whereEF (EF = 0 eV) is the Fermi level and EDirac is the Diracpoint inside the graphene contact regions. The broadening ofDOS is captured by a phenomenological approach [15]–[18]with an M–G coupling strength of Δ (in millielectronvolts) thatcan reproduce the ab initio simulation results [17]. The effectof M–G contacts on the channel region is captured througha contact self-energy function ΣS,D = τgSτ †, where τ is the

coupling matrix between the contact and the channel (τ † is itsHermitian conjugate) and gS is the surface Green’s functionof the contact, gS(E) = [(E + iΔ)I − Hcontact]−1 [16]. Here,Hcontact is the contact Hamiltonian matrix, and I is the identitymatrix. In the mode-space approach, gS of the qth mode canbe analytically expressed as the equation of gsq shown at thebottom of the page. The source contact self-energy functionfor the qth mode is Σ1,1

Sq = (b1q)2gsq, where b1q = t0 andb2q = 2t0cos(qπ/(n + 1)) are the coupling parameters in theqth mode 1-D sublattice, t0 is the nearest neighbor tight-bindingparameter, n is the number of carbon atoms in the width direc-tion, and U1 is the electrostatic potential at the source end [29].A similar expression applies for the drain contact self-energyfunction ΣDq, with U1 being replaced by the potential at thedrain end. The retarded Green’s function for qth mode is thendetermined by Gq(E) = [(E + i0+)I − Hq − ΣSq − ΣDq]−1,where Hq is the channel Hamiltonian matrix for the qth mode

[Hq] =

⎡⎢⎣

U1 b2q

b2q U2 b1q

b1q U3 b2q

· · · · · ·

⎤⎥⎦ .

Here, Ui is the electrostatic potential at the ith atom inthe qth mode. The source (drain) local DOS (LDOS) withinthe channel are computed as LDOSS(D) = GqΓS(D)G

†q/2π,

where ΓS(D) = i(ΣS(D) − Σ+S(D)) is the energy broadening

due to the source (drain) contact. The total LDOS withinthe channel is given by the summation of LDOSS andLDOSD. Finally, the channel current is computed fromIDS = (2e/h)

∫T (E)(fS(E) − fD(E))dE, where fS/D are

the source/drain Fermi–Dirac distribution functions, respec-tively, and T (E) =

∑q Tq(E) is the total transmission coef-

ficient with Tq being the transmission of the qth mode.

III. EFFECT OF M–G CONTACT ON THE CHANNEL

To explore the influence of M–G contact on the channel, weplot the energy-position-resolved channel LDOS in logarithmicscale in Fig. 2 for (a) Δ = 0 meV and (b) Δ = 50 meV. Thedevice structure is the same as shown in Fig. 1 with VDS =0 V and VGS = 0.1 V. The potential profiles of the channelDirac point (dashed lines) are the self-consistent results. Thechannel Dirac point at the source and drain ends are equalto 0.2 eV, which shows the p-type doping effect inside thecontact with ΔEcontact = −0.2 eV. When Δ = 0 meV, LDOSnear the contact Dirac point energy level (0.2 eV) is very low(darker color). As mentioned in Section II, states within thechannel are given by LDOSS(D) = GqΓS(D)G

†q/2π. When

Δ = 0 meV, the contact broadening effect ΓS(D) ≈ 0 leadsto a negligible broadening of the channel states. Even thoughstates do exist within the channel, those states with infinitesimal

gsq =(E − U1 + iΔ)2 + b2

1q − b22q +

√[(E − U1 + iΔ)2 + b2

1q − b22q

]2 − 4(E − U1 + iΔ)2b21q

2b21q(E − U1 + iΔ)


Fig. 2. Energy-position-resolved channel LDOS at VDS = 0 V and VG = 0.1 V, ΔEcontact = −0.2 eV. (a) When Δ = 0 meV, LDOS along the contact Diracpoint at 0.2 eV are unobservable due to a contact which induced a negligible broadening when ΓS(D) ≈ 0. (b) When Δ = 50 meV, the broadening effect ΓS(D)is large, and then, the states near 0.2 eV are broadened and can be observed. LDOS versus energy plot (c) at source end of the channel and (d) at middle of thechannel for different Δ. Inset figure shows the channel LDOS at −0.09 eV, comparing with Lch = 300, when Lch = 15 nm LDOS along the channel increasedue to contact-induced states.

broadening are not visible in the energy-position-resolvedLDOS. However, when Δ = 50 meV, ΓS(D) is large, whichgives obvious broadening effect of the channel states. Thus,energy-position-resolved LDOS clearly shows states near theenergy level of the contact Dirac point in Fig. 2(b). Near thegate-controlled channel Dirac point at about −0.09 eV, contact-induced evanescent states can be observed penetrating into thechannel. Those states originate from the wave functions inci-dent from the contacts. Because graphene has a zero bandgap,those evanescent states can penetrate for a long distance.

Fig. 2(c) and (d) show LDOS versus energy at the sourceend of the channel and at the middle of the channel for two Δvalues. It is clear that, at Δ = 0 meV, a negligible ΓS(D) willlead to unobservable states at the energy level of the contactDirac point. M–G coupling can broaden the zero DOS near thecontact Dirac point, but the effect of broadening is weak if theintrinsic graphene DOS is large [sketch of intrinsic DOS solidline and broadened DOS dashed line in Fig. 2(b)]. Along thechannel Dirac point at around −0.09 eV, the MIS inside thechannel is negligible; thus, LDOS does not have a dependenceon Δ. Contact-induced evanescent states will affect the channelLDOS, but the effect of MIS due to M–G coupling Δ is trivial.Golizadeh–Mojarad’s work [15] shows that, without any bias,the contact Dirac point is at the same energy level as thechannel Dirac point. MIS along the channel Dirac point showsstrong dependence on M–G coupling Δ. This conclusion isvalid if no bias is added and contact Fermi level is fixed at theDirac point. Our work provides a complete description sincethe metal-induced contact doping effect is captured, and thepotential profile is solved self-consistently at any given bias.

The calculated LDOS inside the channel is the summation ofthe intrinsic graphene DOS and states due to contact incidentwave-function penetration. The inset of Fig. 2(c) shows that,at Lch = 15 nm, contact incident wave functions increase thechannel LDOS, which has a large influence on the minimumcurrent as discussed later.

IV. RESULTS AND DISCUSSION

Fig. 3 shows the calculated transfer characteristics (T =300 K) at low drain bias VDS = 0.1 V with different Fermilevel alignments ΔEcontact in the contact regions. The M–Gcoupling strength is taken to be Δ = 50 meV. The effectsof different Δ’s are discussed later. If ΔEcontact = 0 eV,graphene contact is not doped by metal, and the transfer curveis symmetric as shown in Fig. 3(a). The minimum conductionpoint is located at gate voltage VG = VDS/2. In Fig. 3(b),ΔEcontact = −0.2 eV (p-type doping), a typical value for Aucontact is based on [11]. At negative VG, carriers can directlygo through the channel. At positive VG, the electrons need to gothrough the channel Dirac point (see schematic potential of theDirac point). Because DOS near the Dirac point is very low, itsuppresses the carrier injection from contact to channel. Thus,the positive current branch is reduced compared to the negativebranch. The complete transfer curve shows a clear asymmetricbehavior. We point out that the gate voltage at which theminimum conduction point occurs is also slightly shifted dueto the asymmetric barriers at the contacts. When ΔEcontact ispositive as in Fig. 3(c), an effective n-type doping is introducedby the metal contacts. A similar asymmetric behavior with the


Fig. 3. Transfer characteristics under different ΔEcontact. (a) Without any shift of Fermi level in the contact region, symmetric transfer characteristics can beseen. When the Fermi level of contact regions of graphene is shifted due to the metal contact as shown in (b) ΔEcontact = −0.2 eV and (c) ΔEcontact = 0.2 eV,asymmetric transfer characteristics are observed.

positive current branch being greater than the negative branch isseen in that case. Another interesting feature is, compared withIDS–VGS in Fig. 3(a), a contact doping effect that increases theon-current as shown in Fig. 3(b) and (c).

The effect of different coupling strengths Δ’s at VDS = 0.1 Vis shown in Fig. 4. The rigorous explanation of the values usedfor Δ is related to the M–G hybrid system, which is beyondthe focus of this work (see [11] and [12] for details). For acomparison, we define three Δ values here; Δ = 0 eV for theintrinsic graphene, Δ = 8 meV for weak M–G coupling, andΔ = 50 meV for strong coupling. Fig. 4(a) and (b) shows thetransfer characteristics at channel length Lch = 300 and 15 nm,respectively. We observe that the on-current increases for largerΔ, which can be understood by looking at the impact of Δ onT (E) in the ON-state (Fig. 4(c), center panel). First of all, it isseen that, at Δ = 0 eV, there are three distinct minimum pointsin T (E) corresponding to the zero-DOS Dirac point positioninside the channel, source, and drain regions, respectively. Onthe other hand, at larger Δ, T (E) near the source and the drainDirac points increases due to metal-induced DOS broadeninginside the M–G contact regions, which ultimately enhancesthe current transport (Fig. 4(c), right panel). Interestingly, theminimum current Imin, however, does not show a dependenceon Δ. Fig. 4(d) shows the potential profiles of the Dirac point(left), T (E) (center), and the energy-resolved current densityJ(E) (right) at the minimum conduction point of Lch = 15 nmdevice. Although the DOS of the graphene contact is broadenedby the metal contact, T (E) in the current-carrying energywindow between the source Fermi level EFS and the drainFermi level EFD remains the same for different Δ values. AtLch = 15 nm, direct source-to-drain (S → D) tunneling is thedominant factor controlling Imin. Furthermore, it is necessaryto point out that the aforementioned interesting features due tovarious Δ’s still remain valid with other oxide thickness and di-electric values, since the aforementioned effects are mainly dueto contact DOS broadening. Here, transfer characteristics withtox = 5 nm, εox = 9, and Δ = 50 meV (solid lines) are shownin order to compare different EOT values. When EOT increases,the current decreases. The current reduction is due to the lossof CG and longer effective electrostatic scaling length at larger

EOT [24]. At large positive and negative VGS, CQ is large, andsince CG = (CoxCQ)/(Cox + CQ), CG is dominated by Cox.When EOT increases, Cox decreases; thus, the loss of CG is themain reason leading to current reduction. On the other hand,at small VGS, CQ is small and dominant. The drop in CG issmall, and longer effective electrostatic scaling length furtherlimits the current. In addition, when EOT increases, the longereffective electrostatic scaling length increases the asymmetryin the IDS–VGS characteristics. Short-channel effects can alsobe observed with large EOT. At Lch = 15 nm, the minimumconduction point shifts about 0.15 V, while at Lch = 300 nm,such shifts are very small.

Fig. 5(a) and (b) shows a comparison of the effect of differentcoupling strengths Δ’s at large VDS = 0.3 V. When Δ = 0 eV,in addition to the primary minimum conduction point, a distor-tion appears in the ID–VGS characteristics. The two minima aredue to the misalignment of the Dirac point of the channel anddrain regions. With VDS = 0.3 V, the drain Dirac point locatesbetween EFS and EFD. The channel Dirac point is controlledby the gate. At VG1 = −0.05 V, all carriers pass through thechannel hole cone, and at VG2 = 0.1 V, carriers move throughthe channel electron cone. However, at VG = 0.025 V, bothelectron and hole cones are involved; thus, the channel Diracpoint leads to a local minimum. When Δ = 50 meV, DOSnear the contact Dirac point are broadened. The only mini-mum conduction point is due to the channel Dirac point, andthe distortion disappears. A recent experimental work reportsthe presence of this type of distortion before annealing and thedisappearance of the distortion after annealing [30]. Our modelexplains this behavior without resorting to new postulates (suchas charge depinning at metal contacts as proposed in [30]).Before annealing, the M–G interface is not clean, and thecoupling is weak. After annealing, better M–G coupling isachieved, and the distortion disappears. In contrast to the low-VDS case in Fig. 4, Imin at large VDS shows a dependenceon Δ. Fig. 5(d) shows the internal transport properties nearthe minimum conduction point of Lch = 15 nm GFET. Inthis case, at large VDS, the Dirac point in the drain region islocated between EFS and EFD. The broadened DOS in thedrain contact at larger Δ increases J(E) and, thus, the Imin


Fig. 4. Effect of different coupling strength Δ at VDS = 0.1 V. On-current increases at larger Δ for both (a) Lch = 300 nm and (b) Lch = 15 nm. The solid linesare the transfer characteristics with tox = 5 nm, εox = 9, and Δ = 50 meV. When EOT increases, the minimum conduction point shifts due to the short-channeleffect. (c) Increase of on-current corresponds to the broadened DOS of the graphene contact. However, Imin does not change with Δ even at Lch = 15 nm.(d) T (E) between EFS and EFD does not depend on Δ, suggesting that direct S → D tunneling is the dominant factor.

does as well. On the other hand, T (E) near the channel Diracpoint energy at about −0.3 eV does not show a dependenceon Δ. Thus, the increase in Imin can be attributed to the DOSbroadening in the contacts. Here, we point out that the “large-VDS” condition is determined by |VDS| > |(EF − ED)/q| thatwould increase Imin at larger Δ values.

The performance of GFETs upon scaling of the channellength is crucial for technology scaling, which is discussedin Fig. 6. Our model assumes a high-k insulator to obtainsuperior electrostatic gate control to avoid the short-channeleffect. In Fig. 6, Δ = 50 meV, and Ion remains almost thesame for different channel lengths, but Imin increases at shortLch. At short channel lengths, Imin is mainly affected by directS → D tunneling. Here, when Lch is reduced from 150 to40 nm, because the probability for S → D tunneling rises,Imin increases by about 10%. When Lch = 15 nm, S → Dtunneling becomes more severe, and Imin increases by 1.5 timescompared with Lch = 150 nm. A similar scaling behaviorpersists even at VDS = 0.3 V, and Imin increases by 20% whenthe channel length shrinks from 150 to 15 nm (not shown).

The ID versus VDS characteristics are shown in Fig. 7 for (a)VGS > 0 V and (b) VGS ≤ 0 V. ΔEcontact = 0.5 eV is assumedas a degenerate n-type contact. The IDS–VDS characteristics atVGS = 0.2 V and VGS = 0.4 V in Fig. 7(a) show a kink char-acteristic due to an ambipolar channel, which is also observedin the experiments [6]. In the unipolar regime, where VDS <VDS,kink, the GFET shows saturating characteristics [6]. WithVGS > 0 V, the source/channel/drain are all n-type and com-prise an n-n-n-type structure, electrons will directly transportthrough the channel, and, thus, the dependence of the contactDOS and M–G coupling strength Δ is small. With VGS ≤ 0 Vin (b), at weak coupling as Δ = 0 meV, a saturation behaviorhas been observed. The reason for this saturation behavior isbecause VGS ≤ 0 V leads to a p-type channel and an n-p-n-type structure, and the n-type contact needs to inject electronsinto the channel. When Δ = 0 meV, low-contact DOS nearthe Dirac point limits the carrier injection from the contacts.With large Δ, contact DOS is broadened, and the saturationbehavior disappears, which is similar to large Δ increasing theon-current in Fig. 5.


Fig. 5. Effect of different coupling strength Δ at VDS = 0.3 V. Aside from the minimum conduction point at about 0.2 V, a distortion appears when (triangle)Δ = 8 meV and (pentagram) Δ = 0 meV. Considering intrinsic graphene, (c) shows the source, drain, and the channel DOS (cartoon) in series which decidehow the total carriers transport through the channel. When electron and hole cones are both involved in the transport at VG = 0.025 V, a local minimum is given.As Δ increases, the DOS of graphene contact are broadened, and distortion disappears. (d) For Lch = 15 nm at the minimum conduction point VG = 0.3 V, thedrain Dirac point is located between EFS and EFD; large Δ broadens the DOS at the drain contact, increasing the T (E) and Imin.

Finally, we want to discuss the device performance opti-mization considering the influence of M–G contact. In Fig. 5,we point out that the broadening of DOS in contacts willincrease the Imin at large VDS. Thus, to avoid Imin currentincrease due to DOS broadening, the drain bias needs to satisfy|VDS| < |(EF − ED)/q|. On-current is benefited from strongM–G coupling as shown in Fig. 4. We have also explored thedependence on different ΔEcontact (not shown). If |ΔEcontact|is large, the metal-induced doping effect becomes stronger, theon-current will increase, and Imin can be controlled with appro-priate VDS. Metals with large work-function difference com-pared to graphene could be a good candidate to provide large|ΔEcontact| values [11], [12]. The other important issue is thatthe gate electrostatics play a crucial role. With only the backgate, very long band bending length (long effective electrosta-tic scaling length) near the contacts has been experimentally

observed [20]–[22]. Our simulation here is based on excellenttop gate electrostatics; thus, the band bending length is small,which helps to control the Imin while increasing the on-current.

A recent paper has explored the performance of 2-D GFETsunder ballistic limits [31]. In [31], the contact self-energy isassumed to be constant and independent of energy, whichis a good approximation when a metal destroys the lineardispersion of graphene [11]. Our model uses a differentapproach to describe the contact, where the contact self-energydepends on the coupling strength Δ. Using Δ as a variableparameter, additional interesting effects have been discussed inthis paper. When Δ is small, the linear dispersion of graphenestill exists [11], [17]. If the coupling strength Δ furtherincreases to about 0.3 eV, the graphene contact will becomemetallic-like, and we can also obtain similar results as the puremetal contact case [18].


Fig. 6. Effect of channel length scaling at VDS = 0.1 V. A high-k insulator is used to avoid the short-channel effect. Ion stays the same when Lch is scaleddown. As Lch is reduced from 150 to 40 nm, Imin increases by 10% due to the direct S → D tunneling. When Lch = 15 nm, direct S → D tunneling becomesmore severe, and Imin increases by about 1.5 times.

Fig. 7. Effect of coupling strength Δ on the IDS versus VDS characteristics. ΔEcontact = 0.5 eV as the heavily doped n-type contact, and Lch = 100 nm.The ID versus VD is grouped into two areas: (a) VGS > 0 V and (b) VGS ≤ 0 V. (a) shows a kink characteristics with the saturation region due to an ambipolarchannel. Influence of Δ is small. With VG ≤ 0 V in (b), with weak coupling as Δ = 0 meV, the saturation behavior has been captured. With large Δ, thesaturation behavior disappears.

V. CONCLUSION

In this paper, we have used detailed numerical simulationsto investigate the impact of metal contacts on the operationof GFETs with electrostatically well-designed top gates. Themetal contacts introduce two effects: 1) The Fermi level ofgraphene underneath the metal is shifted, resulting in asym-metric transfer characteristics, and 2) the DOS of grapheneinside the contacts is broadened. Δ is introduced to describethe broadening of the DOS inside the M–G contacts. Basedon our results, a weak coupling of metal contacts can causea distortion of the transfer characteristics, which disappears at

strong coupling strengths. Large Δ broadens the contact DOSand increases the Ion but does not affect Imin at low VDS.At large VDS, i.e., |VDS| > |(EF − ED)/q|, DOS broadening(MIS inside the contacts) increases both Ion and Imin. Withscaling of channel length, direct S → D tunneling is the crucialfactor that increases Imin at short channel lengths.

ACKNOWLEDGMENT

The authors would like to thank Prof. Z. Chen of PurdueUniversity for many fruitful discussions.


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Pei Zhao (S’08) received the B.S. degree in elec-tronic engineering from Huazhong University of Sci-ence and Technology, Wuhan, China, in 2007 and theM.S. degree in electrical and computer engineeringfrom the University of Florida, Gainesville, in 2009.He is currently working toward the Ph.D. degreein electrical engineering at the University of NotreDame, Notre Dame, IN.

His current research work focuses on devicephysics, modeling, and fabrication of nanoscaletransistor.

Qin Zhang (M’09) received the B.S. degree inelectronic engineering from Tsinghua University,Beijing, China, in 2003 and the M.S. and Ph.D.degrees in electrical engineering from the Universityof Notre Dame, Notre Dame, IN, in 2005 and 2009,respectively.

As a recipient of the NIST/MIND PostdoctoralFellowship, she is currently with the Semiconduc-tor Electronics Division, NIST, Gaithersburg, MD.Her research interests include tunneling devices andgraphene electronics.

Debdeep Jena received the B.Tech. degree witha major in electrical engineering and a minor inphysics from the Indian Institute of Technology,Kanpur, India, in 1998 and the Ph.D. degree in elec-trical and computer engineering from the Universityof California, Santa Barbara, in 2003.

Since 2003, he has been with the faculty of theDepartment of Electrical Engineering, University ofNotre Dame, Notre Dame, IN. His research andteaching interests are in the MBE growth and deviceapplications of quantum semiconductor heterostruc-

tures (currently III–V nitride semiconductors), investigation of charge transportin nanostructured semiconducting materials such as graphene, nanowires, andnanocrystals, and their device applications, and in the theory of charge, heat,and spin transport in nanomaterials.


Siyuranga O. Koswatta received the B.S. degree incomputer engineering (summa cum laude) from theUniversity of Bridgeport, Bridgeport, CT, in 2002and the M.S. and Ph.D. degrees in electrical andcomputer engineering from Purdue University, WestLafayette, IN, in 2004 and 2008, respectively.

Since 2008, he has been with the IBM T. J. WatsonResearch Center, Yorktown Heights, NY, as a Re-search Staff Member. From 2009 to 2010, he waswith the University of Notre Dame, Notre Dame,IN, as the IBM assignee to the Midwest Institute

for Nanoelectronics Discovery (MIND). His research interests include mod-eling and simulation of exploratory devices for nanoelectronic applications.He has been investigating band-to-band-tunneling-based transistors for low-power electronics and carbon-nanotube- and graphene-based low-dimensionaldevices.

inﬂuence of metal–graphene contact on the operation and ......metal-induced gap states in...

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